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-- NASA TECHNICAL NOTE N o* m P n z NASA TN D-4592 L. / --I " LOAN COPY: RETU!?N IO AFWL (WLIL-2) KIRTLANO AFB, N MEX CAVITATING PERFORMANCE OF TWO LOW=AREA=RATIOWATER JET PUMPS HAVING THROAT LENGTHS OF 7.25 DIAMETERS NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. MAY 1968 c https://ntrs.nasa.gov/search.jsp?R=19680014989 2019-01-02T04:46:52+00:00Z
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Page 1: NASA TECHNICAL NOTE -- NASA TN D-4592

-- NASA TECHNICAL NOTE

N o* m P n z

N A S A TN D-4592

L. / --I"

LOAN COPY: RETU!?N I O AFWL (WLIL-2)

KIRTLANO AFB, N MEX

CAVITATING PERFORMANCE OF TWO LOW=AREA=RATIOWATER JET PUMPS HAVING THROAT LENGTHS OF 7.25 DIAMETERS

N A T I O N A L A E R O N A U T I C S A N D SPACE A D M I N I S T R A T I O N W A S H I N G T O N , D. C. MAY 1 9 6 8

c

https://ntrs.nasa.gov/search.jsp?R=19680014989 2019-01-02T04:46:52+00:00Z

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-

'TECH LIBRARY KAFB. NM

0333049 NASA T N D - 4 3 Y Z

CAVITATING PERFORMANCE OF TWO LOW-AREA-RATIO WATER J E T

PUMPS HAVING THROAT LENGTHS OF 7.25 DIAMETERS

By Nelson L. Sanger

Lewis Research Center Cleveland, Ohio

NATIONAL AERONAUT ICs AND SPACE ADMlN ISTRATION ~

For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTI price $3.00

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-11111111111111 1111

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.

CONTENTS

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MECHANISM AND ANALYSIS OF CAVITATION . . . . . . . . . . . . . . . . . . .

Mechanism of Cavitation in Jet Pump Flow . . . . . . . . . . . . . . . . . . . . Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Previously reported analyses . . . . . . . . . . . . . . . . . . . . . . . . . . Present analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

APPARATUS AND PROCEDURE . . . . . . . . . . . . . . . . . . . . . . . . . . . Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cavitation Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Air content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Incipience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time delay effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noncavitating Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overall Cavitating Performance . . . . . . . . . . . . . . . . . . . . . . . . . .

Effect of Flow ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of nozzle spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photographs of cavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Prediction Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cavitation prediction parameter . . . . . . . . . . . . . . . . . . . . . . . . .

Effect of nozzle spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison with previously reported resul ts . . . . . . . . . . . . . . . . .

Alternate cavitation prediction parameter . . . . . . . . . . . . . . . . . . . . SUMMARY OF RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . APPE NDME S

A-SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B .DEVELOPMENT OF J E T PUMP CAVITATION ANALYSES . . . . . . . . . .

I. Gosline and O'Brien Analysis . . . . . . . . . . . . . . . . . . . . . . . . 11. Rouse Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. Bonnington Modified Rouse Parameter . . . . . . . . . . . . . . . . . . . IV . Cavitation Prediction Parameter . . . . . . . . . . . . . . . . . . . . . . V . Alternate Cavitation Prediction Parameter . . . . . . . . . . . . . . . . .

REFERENCES

Page 1

2

7 7 9 9 9 10 10

10 10 12 15 16 18 21 21 22 22 24

26

28 30 30 32 32 33 35

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CAVITATING PERFORMANCE OF TWO LOW-AREA-RATIO WATER JET

PUMPS HAVING THROAT LENGTHS OF 7.25 DIAMETERS

by Nelson L. Sanger

Lewis Research Center

SUMMARY

Cavitation performance (total headrise as a function of pumped fluid inlet pressure) of two jet pumps was evaluated in a closed-loop facility using room-temperature, deaer­ated water. Objectives of the investigation were to study the cavitation performance of jet pumps having low ratios of nozzle to throat area and to examine methods of cavitation prediction in jet pumps.

Experimental performance was obtained with two nozzles operated separately in one tes t section. The test section had a throat diameter of 1. 35 inches (3 .43 cm), a throat length of 7 .25 diameters, and a diffuser included angle of 8'6' (0.141 rad). The nozzles had exit diameters corresponding to nozzle- to throat-area rat ios of 0.066 and 0.197. Each nozzle was operated at three spacings of the nozzle exit from the throat entrance. At each nozzle spacing, tes t s were conducted at four values of seconary- to primary-flow ratio, while secondary (pumped fluid) inlet pressure was varied.

Extensive amounts of cavitation were observed before performance was affected. However, when the head ratio deteriorated, it did s o quite sharply. At a fixed nozzle position, an increase in secondary- to primary-flow ratio resulted in a greater required secondary fluid inlet pressure in order to suppress cavitation. At any fixed flow ratio, less secondary fluid inlet pressure was required to suppress cavitation as the nozzle was retracted from the throat entrance.

For the test section considered in this investigation, a nozzle spacing of approxi­mately 1throat diameter best satisfied the two major performance requirements of high efficiency and cavitation resistance. The design of the secondary inlet region was im-

Smooth hydrodynamic streamlining of thisportant to jet pump cavitation performance. region and a thin nozzle wall at the nozzle exit would reduce cavitation susceptibility.

Two related parameters are proposed which are useful in predicting the conditions at which total headrise deteriorates because of cavitation.

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I NTRODUCTlON

Future space vehicles will require large quantities of electric power. One means of meeting these requirements is through the use of a Rankine cycle system having a liquid metal as the working fluid. Jet pumps have several possible applications in such systems (refs. 1 to 3). In order to achieve high system efficiencies, high boiler temperatures and pressures and low radiator temperatures and pressures are necessary. This combination, in addition to a requirement for low power absorption by the jet pump, resul ts in jet pumps having low ratios of nozzle exit area to throat area (jet pump area ratio R). J e t pumps having low area ratios require a relatively low quantity of flow to be recirculated to the nozzle by the main-stage pump (primary or high pressure "booster" flow Q1), thus keeping the main-stage-pump size, weight, and power requirements low.

In a previous report , jet pump design considerations were explored, both analytically and experimentally, for the case of noncavitating operation (ref. 3). However, in Rankine cycle space systems, cavitation in the pumps represents a ser ious problem. Radiator condensate pumps and boiler recirculation pumps must handle fluid quite near saturation temperature. Cavitation can be suppressed by subcooling the fluid. But utilizing subcool­ing as the only method of cavitation supression resul ts in an unacceptable system weight penalty due to the need for additional radiator-condenser sections. One solution to this problem is the use of a limited amount of subcooling and a cavitation-resistant auxiliary pump to boost inlet pressure to the main-stage pump. If a jet pump is used as an auxiliary unit, or in certain applications as a main-stage unit, a knowledge of je t pump cavitation performance will be necessary to optimize system weight and performance.

No single method of predicting the cavitation-imposed operating l imits of jet pumps has yet been agreed on. The mechanism of cavitation in a jet pump is closely related to the turbulent mixing process. This process is not yet fully understood, particularly for the case of a ducted jet.

Jet pump cavitation was first discussed in reference 4 for the condition at which cavi­tation caused total headrise to drop off. Limiting secondary (pumped) flow Q2 was pre­dicted by application of the one -dimensional energy and continuity relations. With room-temperature water as the test fluid, a general but uneven correlation between theory and experiment was achieved. Rouse (ref. 5), working also with room-temperature water, investigated cavitation produced by a submerged jet ejecting into a large tank of quiescent water. He was able to correlate audible incipient cavitation at different flow rates by using a conventional cavitation number. In reference 6, Bonnington attempted to modify the Rouse parameter to apply to the ducted flow of a jet pump. H i s experimental data, which corresponded to the condition of total headrise dropoff and not incipience, did not correlate with the modified Rouse parameter. Contrary to these results, experimental data published by Mueller (ref. 7), also for the condition of total headrise dropoff, agreed

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with the modified Rouse parameter. Other cavitation prediction parameters have been suggested (refs. 8 and 9) but have not been used widely. A summary presentation of these parameters is given in reference 7.

The present investigation was conducted to study the cavitation performance of jet pumps having low area ratios and to examine methods of cavitation prediction in je t pumps further. Specifically, cavitation performance was investigated in t e rms of the charac­terist ics of the je t pump total headrise at constant values of secondary- to primary-flow rat io M as the inlet p ressure of the secondary fluid Q2 was reduced. Although the conditions at which total headrise deteriorated were of principal interest, performance conditions were obtained for all stages of cavitation.

Experimental performance at two area ratios, R = 0.197 and 0.066, was recorded by operating two nozzles separately in one test section. Three different spacings of the noz­zle exit upstream from the throat entrance were investigated for each area ratio. De­aerated, room-temperature tap water was used as the test fluid. The acrylic plastic test section was constructed with a circular bell-mouth entry, a constant diameter throat having a length of 7.25 diameters, and a diffuser of 8'6' (0.141 rad) included angle. Operating conditions included pr imary flow rates of 33 and 75 gallons per minute (2.08 and 4 . 7 4 ~ 1 0 - ~m3/sec), secondary flow ra tes of 85 to 150 gallons per minute (5.36 to 9 . 4 7 ~ 1 0 ~ ~m3/sec), and secondary inlet pressures of 4 to 25 pounds per square inch absolute (2. 76 to 17. 2X104 N/m2 abs).

MECHANISM AND ANALYSIS OF CAVITATION

Mechanism of Cavitat ion in Jet Pump Flow

To interpret experimental resul ts accurately requires some knowledge of the mecha­nism of cavitation inception and development in a jet pump. As defined by Holl and Wislicenus (ref. lo), "The term cavitation shall denote the formation of vapor or gas filled voids within a liquid under the influence of local pressure reductions produced by dynamic action. '' The model of cavitation inception that has gained the widest acceptance is the nuclei theory (ref. 11). Theoretical analyses (ref. 12) predict that a pure liquid can sustain considerable tensile stress before fracturing. Experimental investigations of highly purified and deaerated water (refs. 13 and 14) have confirmed the existence of liquid tension, but of a magnitude less than theoretically predicted. Other investigations (refs. 15 and 16), which used unmodified water, have reported even smaller tensions,

2but still of the order of several pounds per square inch (N/m ). This inability of a liquid to sustain theoretically predicted tensions has been attri­

buted to the presence of "weak spots" or nuclei. A liquid under tension is metastable,

3

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and nuclei of sufficient size provide the required disturbance to produce instability. The nuclei have been hypothesized as consisting of smal l volumes of undissolved gas present i n crevices of the boundary material and in crevices of microscopic dust particles present in the free s t ream. A nucleus of sufficient s ize exposed to a pressure lower than a crit ical value grows rapidly. Exposure need only be for short time intervals (e. g. , 10 psec for a spherical bubble 0.001 in. (0.0025 cm) in diameter, ref. 17) to initiate the process.

For the case of unseparated flow, in which the minimum pressure occurs at the bound­ary , it has generally been possible, with the exception of certain scale effects (ref. lo ) , to predict cavitation inception with the aid of the conventional cavitation number. The use of fluid vapor pressure as crit ical pressure has proved successful for most engineering applications (ref. 11). In separated flow and shear flow, however, the minimum pressure does not occur at the boundary but in the shear layer, and experimental results have had to be relied on as the chief source of information. In reference 18, the turbulence level in boundary-layer flow was related to cavitation inception. Incipient cavitation was ob­served to occur in the center of the boundary layer. This suggests that nuclei were being transported from the wall to the center of the vortical eddies in the turbulent boundary layer.

Flow in a jet pump is of the shear type. The primary and secondary fluids are separated by a shear or mixing layer composed of many small turbulent eddies. The experiments of reference 4 confirmed the existence of low local pressures related to turbulence in jet mixing layers. Cavitation occurs in the mixing layer, and it is likely that the mechanism of occurrence is identical to that observed in turbulent boundary layers, with the exception of the source of the nuclei. In the experiments of reference 18, the source of nuclei was the wall next to the boundary layer. In jet pumps, there a r e two likely sources: f ree-s t ream nuclei, and nuclei transported by the boundary layer flowing over the primary nozzle surfaces.

Analysis

Because the flow in a jet pump is a shear flow, cavitation inception conditions a r e not readily predicted. Not enough is presently known of the relation between the minimum local pressures in the mixing layer and important jet pump flow parameters. In jet pump flow, however, cavitation inception is not of pr imary interest. The conditions at which jet pump total headrise deteriorates as a result of cavitation a r e the more cri t ical condi­tions from the standpoint of design and application.

The nomenclature used in the following discussion of analyses is established in figure 1 and appendix A . The primary fluid Q1 is pressurized by an independent source

4

I

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t- -Throat -14 -Diffuser +

I Secondary]fluid CD-9399

Figure 1. - Schematic representation of jet pump.

and is accelerated to high velocity in the primary nozzle. In a Rankine cycle system, in which the jet pump is used as a n auxiliary pump to the condensate pump, the primary fluid is the recirculated fluid, sometimes referred to as the "booster" flow. The secondary fluid is the pumped fluid and is entrained by and mixed with the high-velocity primary fluid in the constant-diameter throat section. The mixed fluids pass through a diffuser which converts a part of the velocity head to static pressure. In a Rankine cycle system application, the secondary flow rate is equivalent to the flow rate through the main cycle.

J e t pump performance is commonly expressed by the following parameters: the secondary- to primary-flow ratio, M = Q2 1; the head ratio, N = (H5 - H2)/(H1 - H5);/Q and the nozzle- to throat-area ratio, R = An/At.

Previously reported analyses. - The analysis of reference 4 did not attempt to account for the character of the mixing process nor conditions at cavitation inception. The analysis is presented in appendix B section I by using nomenclature convenient to this report . Application of the energy and continuity relations to the secondary fluid results in an expression for secondary flow rate. The assumption was made that, at the point of total headrise breakdown due to cavitation, the pressure in the plane of the pr imary nozzle was equivalent to vapor pressure at the inlet temperature of the secondary fluid. The resulting expression for Q2 is the maximum attainable secondary flow rate.

In reference 5, Rouse conducted a n experimental investigation of cavitation inception in a free jet, using water as the test fluid. The parameter employed was the conventional cavitation number (appendix B section 11)in which the correlating pressure was the pres­sure in the field surrounding the nozzle pF, and the reference velocity was the nozzle exit velocity. Because a free jet was investigated, the pressure pF remained constant

5

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throughout the mixing region, and the "secondary" fluid was entrained from the rest. A value of the cavitation parameter oR = 0.6 correlated audible incipient cavitation over a range of flow rates. Rouse recognized the influence of turbulence in the mixing zone on the mechanism of cavitation. But he also pointed out the difficulties involved in construct­ing an accurate prediction index based on turbulence parameters (e. g. , the nonisotropic character of turbulence in the mixing zone, the experimental problem of measuring the parameters , and the question of whether it is the r m s or average negative peak pressure that is significant in the process).

A modification of the Rouse parameter was introduced by Bonnington (ref. 6) to account for the influence of the bounding walls on the je t i n a je t pump (appendix B section m). It is debatable whether the physics of the mixing process permit such a facile transformation from the case of f ree to ducted jets. It is even more questionable whether the value of oR = 0.6, determined for the case of incipient cavitation in a free jet, can be properly used to predict the point of cavitation-induced head breakdown in a jet pump. The experimental resul ts of reference 6 did not correlate with the modified parameter but did produce a regular correlation with the velocity ratio V3/Vn. However, in reference 7, data were presented (for the point of performance breakdown) which cor­related closely with the modified Rouse parameter. There was thus a direct contradic­tion between the experimental results of reference 6 and reference 7. The differences and the reasons for them are discussed in the section Cavitation ~. -prediction parameter­(P. 21).

Present analysis. - In appendix B section IV, a parameter is developed which brings together the two analyses set forth by Gosline and O'Brien (ref. 4) and by Bonnington (ref. 6). The energy and continuity relations are applied to the secondary fluid, and the resulting expressions a r e made dimensionless by dividing by the velocity head of the primary fluid at the nozzle exit. It is assumed that at the condition of total headrise breakdown, the pressure in the plane of the nozzle exit p3 will be equal to vapor pressure. The resulting expression at the point of total headrise deterioration

is essentially the expression that Mueller noted would correlate Bonnington's data. It is a lso closely related to the parameter used by Gosline and O'Brien.

6

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APPARATUS AND PROCEDURE

Apparatus

The facility used in. these tests was the same as that described in reference 3. A schematic diagram of the facility is shown in figure 2. Working fluid w a s deaerated tap water continuously filtered to remove particles larger than 25 microns. System pressure was varied by pressurization of two bladder-type accumulators. The pressuriz­ing medium (air) was therefore never in contact with the working fluid, and the air con­tent was maintained at approximately 3 parts per million.

The test pump was also the same as that used in reference 3. The test section (fig. 3) was fabricated from acrylic plastic to permit visual observation and photographic studies to be made. A 5-inch (12. 7-cm) circular radius bell mouth was used as inlet to a constant diameter (1. 35 in. (3 .43 cm)) throat section having a length of 7.25 throat diameters. The throat was followed by a conical diffuser having an included angle of 8'6' (0.141 rad) and an outlet- to inlet-area ratio of 7.73. Static pressure taps of 0.020 inch (0.051 cm) in diameter were installed at 18 axial locations: two in the second­a r y inlet region, nine in the throat, and seven in the diffuser.

Two nozzles were used in conjunction with the test section and a r e shown in figure 4. Nozzle spacing (distance from nozzle exit to throat entrance) was varied by inserting shims between the nozzle flange and a reference surface on the secondary plenum.

Water supply

CD-9401 Figure 2. - Schematic drawing of water jet pump test facility.

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- - - -

-Static pressure taps

Throat Diffuser

-_T Total

-1 probes pressure

in le t

FSecondary

h r o a t T - Diffuser Nozzle to throat axial spacing-,

---'. Z, 9.81 (24.9) Ld, 16.9(42.9)

Test section (acryl ic plastic)--,

Figure 3. - Schematic diagram of test pump and location of static pressure taps and total pressure probes. Diffuser area ratio, (d5ldt)*, 7.73. (Al l dimensions are in inches (cm).)

10.41 (26.43)-­

11.82 (30.0)--

Figure 4. - Jet pump primary nozzles. (All dimensions are in inches (cm).)

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The primary fluid inlet p ressure was read on a Bourdon tube gage. All other pres­su res used for data reduction were measured on manometers.

Pr imary and secondary flow rates were measured by turbine flowmeters. The total flow rate was measured by a venturi flowmeter. The venturi-measured flow rate gener­ally agreed within 52 percent with the sum of the primary and secondary flow rates.

Air content was measured with a Van Slyke Gas Apparatus. Photographs of cavita­tion were obtained with a 70-millimeter still camera coupled to a flash unit.

The estimated e r r o r (instrument and readability combined) of the principal mea­sured variables is listed as follows:

Headrise and static pressures , percent . . . . . . . . . . . . . . . . . . . . . . < rt0. 7 Inlet pressure (primary stream), percent . . . . . . . . . . . . . . . . . . . . . < rt0.6 Flow rate, percent:

Pr imary s t r e a m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . < 4 . 0 Secondary s t ream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . < *2.0

Temperature, O F (OC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . < 52 (*l.1)

Experime ntaI Proced ure

The experimental investigation was conducted with one test section (fig. 3) and two nozzles (fig. 4)having exit diameters corresponding to nozzle- to throat-area ratios of R = 0.066 and 0.197. For each area ratio, several values of secondary- to primary-flow rat io were selected which spanned the flow ratio at the best efficiency point.

For a given value of flow ratio M, the jet pump operating characterist ic defines a corresponding value of head rat io N. If M is held constant, N will a l so remain con­stant as secondary inlet pressure is reduced, until severe cavitation causes either M o r N o r both to deteriorate. For each selected value of flow ratio, secondary inlet pressure P2 was reduced in discrete steps until cavitation caused a sharp drop in per­formance. This procedure was carr ied out at three nozzle spacings for each a rea ratio: one at the fully inserted nozzle position, another at about a spacing of 1 throat diameter, and a third at a large spacing.

Cavitat ion Cr i te r ia

Air content. - Several reports noted that decreasing the air content of test water will reduce the number of nuclei having diameters greater than the cri t ical size for inception. This will resul t in a lower susceptibility to cavitation and will make compari­son of resul ts from different test installations difficult. Space electric power systems,

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however, will be designed to operate with liquid metals as the working fluid. The gas content of these fluids, particularly in the high-temperature liquid-vapor cycles pro­posed, will be extremely low. Thus, these conditions were considered to be simulated best in the water system by reducing gas content to the lowest value practicable.

It should be recognized, however, that although the size and number of f r ee un­dissolved gas bubbles was small , foreign particles up to 25 microns were present. When compared with the size of nuclei required to initiate cavitation, this is not a n exceptionally small size.

Incipience. - Cavitation was produced by reducing secondary inlet pressure while maintaining pr imary and secondary flow rates constant. Principally, it was desired to evaluate the operating conditions fo r which total headrise deteriorated because of cavita­tion. Thus, precise determination of conditions of incipience (e. g. , questions of audible against visible cavitation) was not stressed. Generally, the condition at which cavitation first became visible was recorded. But there was a generous degree of randomness to these points, and there appeared to be no consistent correlation of them. No attempt was made to define the conditions at which cavitation disappeared by increasing the secondary inlet pressure (cavitation desinence).

Time delay effect. - In references 19 and 20, a cavitation time-delay factor was discussed. Holl and Treas te r (ref. 19) observed that, as pressure was decreased, incipient cavitation appeared at a specific pressure only after a finite time had elapsed. Lienhard and Stephenson (ref. 20) related this time delay to a stability phenomenon which controls inception. The time delay was observed during the course of the present jet pump cavitation research. A rapid reduction of inlet p ressure to a preselected level resulted, after a delay of several seconds, in the sudden and violent appearance of cavitation. Consequently, when data runs were taken, the inlet pressure was reduced slowly, and system variables were given time (approximately 1/2 to 1 min) to stabilize before data points were recorded.

RESULTS AND DISCUSSION

Noncavitat ing Performance

Typical noncavitating performance curves from reference 3 are reproduced in fig­u r e 5. Jet pump noncavitating performance is commonly presented nondimensionally as head ratio and efficiency as functions of flow ratio. The efficiencies recorded for both area ratios compare quite favorably with efficiencies reported to date in the l i tera­ture.

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0 28 ( 1 . 7 7 ~ 1 0 - ~ ) 35 (2.21~10-3)

a 63 ( 3 . 9 8 ~ 1 0 - ~ )0 83 (5.24~10'~)

~ Solid svmbols denote head r a t i o 4

K -n I

+ I 13 6 -... 0 1-NI Flow ratio, M = Q21Q1

I= la) Area ratio, 0.066; cavitation data taken at flow ratios of 2.5, 3.5, 4.5, and 5.0.

z .5,

2.0 2.4 Flow ratio, M = Q2/Q1

(b)Area ratio, 0.197; cavitation data taken at flow ratios of 0.9, 1.3. 1.7, and 2.0.

Figure 5. - Noncavitating jet pump performance for two area ratios. Fully inserted nozzle position; nozzle spacing, 0.

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III

Nozzle spacing, sldt

Figure 6. - Noncavitating jet pump performance. Effect of nozzle spacing on maximum efficiency. Cavitation data taken for area rat io of 0.066 at nozzle spacings of 0, 1.05, and 2.58 and for area ratio of 0.197 at nozzle spacings of 0, 0.95, and 2.68.

An important effect investigated in reference 3 was the effect on peak efficiency of the spacing of the nozzle exit from the throat entrance. This effect is summarized in figure 6. For a jet pump having a relatively long throat length (7.25 diam), the most efficient nozzle position was the fully inserted position (s/dt = 0). High values of efficiency were maintained at spacings of up to 1 throat diameter for both area ratios.

Overal l Cavitat ion Performance

Cavitation performance runs were conducted at three nozzle positions for each nozzle- to throat-area ratio. At each nozzle position, characterist ic curves of head ratio N against net positive suction head of the secondary fluid H were obtained at

s, vfour values of secondary- to primary-flow rat io M. The flow ratios chosen were as follows: one corresponding to peak efficiency Mbep, one at a flow ratio less than Mbep, and two at flow rat ios greater than Mbep. The values of flow ratio and nozzle position selected for these tes ts a r e indicated in the figures.

In figure 7, experimental values of head rat io N are plotted as a function of net positive suction head of the secondary fluid Hs, v. Three sets of curves, corresponding to three nozzle positions, a r e shown for each a rea ratio. Each set of curves was obtained at a constant value of primary flow rate Q1. The range of flow ratios, therefore, repre­sents a range of secondary flow rates. Furthermore, the values of H at which total

s, vheadrise deteriorated are applicable only for the flow conditions specified. For the same

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V

.12

I . 10 &-

I i.+ z .08 r .-0­c

E m

2 .06

.04

30 10 10

.02 0

4 -I1I 1

~ 20 8 40 50 0

I l l

20 30 40

Net positive suction head of secondary fluid, Hs, v, fl H20

I I I I I I I I 1 - U 0 2 4 6 8 ,b /4 0 2 4 6 8 10 12

Net positive suction head of secondary fluid, Hs,v, m H20

(a-1) Nozzle spacing, 0. (a-2) Nozzle spacing, 1.05.

10 20 40 Net positive suction head of secondary

fluid, Hs, v, fl H20

I l l 1 1 1 2 4 6 8 1 0 1 2

Net positive suction head of secondary fluid, Hs, ,,, m H20

(a-3) Nozzle spacing, 2.58.

(a) Area ratio, 0.066; pr imary flow rate, 33.0 gallons per minute ( 2 . 0 8 ~ 1 0 - ~m3/sec).

Figure 7. - Effect of net positive suction head and flow rat io on jet pump cavitation performance.

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.4a

.35

.25

z 0­._2 .20 n I­

.15

.10

.05

0 10 50 0 10 20 30 l ive suct head of secondary fluid, Hs, ft H20

I I I L I 1--1-_1 I I I I I 1 0 2 4 6 8 1 0 1 2 1 4 0 2 4 6 8 1 0 12

Net positive suction head of secondary fluid, Hs,v, m H20

(b-1) Nozzle spacing, 0. (b-21 Nozzle spacing, 0.95.

I I

- 1 1

I 50/ Net positive suction head of secondary

fluid, Hs, ,,, fl H20

0-r ! d I(0 1: 14 Net positive suction head of secondary

fluid, Hs, ", m H20

lb-31 Nozzle spacing, 2.68.

(b)Area ratio, 0.197; primary flow rate, 75 gallons per minute ( 4 . 7 4 ~ 1 0 - ~m3/secl.

Figure 7. -Concluded.

14

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Nozzle Area

2.68

2.58

i/7

1­fII

3 5 6 Flow ratio, M = Q2/Q1

Figure 8. - Effect of flow rat io on required net positive suction head.

secondary- to primary-flow ratio, a higher primary flow rate would result in a perform­ance dropoff at a higher value of Hs, v. Arrows mark the approximate pressure level at which visual incipience was noted. Incipient data were not recorded at all flow ratios; therefore, in some cases, no a r rows are indicated.

With few exceptions, the curves show a sharp dropoff in performance due to cavita­tion. No dropoff is indicated at some of the low-flow-ratio conditions. In these cases, the test facility lower limit of secondary inlet pressure, 9 feet (2.74m) of water, was reached before cavitation was developed sufficiently to cause performance deterioration.

Effects of flow ratio. - The curves presented in figure 7 indicate that, for a fixed nozzle position, higher values of secondary inlet head H

s, v were required to prevent total headrise deterioration as flow ratio was increased. This effect of flow ratio on the required net positive suction head is summarized in figure 8, a c ros s plot of figure 7. Although the required H increased with increasing flow ratio, only 10 to 18 feet

s, v(3.05 to 5.5 m) of water were required at the best efficiency flow rat ios (M = 1.4 for R = 0.197 and M = 3.5 for R = 0.066).

The principal reason for the increased susceptibility to cavitation at high flow ratios is evident from a n analysis of the wall static pressure distributions in the test section. These distributions are presented in dimensionless form in figure 9 in te rms of a pressure coefficient. The pressure coefficient is defined by

15

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.-­-4 0 4 8 12 16 20

Axial location f rom throat entrance, xldt

Figure 9. - Effect of flow rat io for nozzle spacing of zero and area rat io of 0.066.

cp= px - p2

Y V i

where the numerator represents the pressure rise above secondary inlet pressure at any axial location in the jet pump, and the denominator is the velocity head of the pr imary fluid at the nozzle exi t .

At a given nozzle position, as flow ratio is increased, lower static pressures are measured in the secondary inlet and throat regions. Since the annular flow a r e a is fixed, for a fixed nozzle position, a n increase in flow rat io causes a n increase in velocity and a corresponding decrease in static pressure. Also, the pressure gradient in the throat is comparatively smal l at high flow ratios. Fluid is exposed to low pressure over a longer period of time, and the tendency for increasing pressure to collapse the cavitation bubbles is reduced.

Effect of nozzle spacing. - Another prominent effect apparent from figure 7 is that cavitation performance improved as the nozzle was retracted. This effect is summarized in figure 10, a cross plot of figure 7. Less net positive suction head was required to prevent performance deterioration as the nozzle was retracted for both a r e a rat ios con­sidered. The reasons for this can be ascertained f rom a n examination of the wall static pressure distributions, for three nozzle spacings, presented in figure 11. For any fixed

16

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I

Nozzle spacing, s/dt

Figure 10. - Effect of nozzle spacing on required net positive suction head of secondary fluid.

4 8 12 16 20~~

Axial location from throat entrance, x/dt

Figure 11. - Effect of nozzle spacing on static pressure distr ibut ion for flow rat io of 3.5 and area rat io of 0.066.

flow condition, it is apparent that, as nozzle spacing is reduced, the level of static pres­sure decreases. This decrease occurs because the annular flow area of the secondary fluid is reduced as the nozzle is moved closer to the throat inlet. An equal amount of flow passing through a smaller area produces higher velocities and lower static pres­sures .

Another factor , of secondary importance, a lso contributes to increased sensitivity to cavitation at small nozzle spacings. In the fully inserted position, the effect of a finite thickness of the nozzle wall at the exit becomes more prominent. In the present

17

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investigation, practical machining requirements resulted in a finite thickness at the exit of each nozzle of 0.027 inch (0.069 cm) (see fig. 4). The fluid dynamic effect of the nozzle wall thickness is the creation of a wake which coincides in location with the shear layer between the two fluids. The wake ac ts to increase the turbulence level of the mixing layer, and therefore to increase susceptibility to cavitation. As the nozzle is retracted into the settling chamber, the effect of nozzle wall thickness is diminished because the static pressure at the nozzle exit plane is higher.

From a n efficiency standpoint, the best nozzle spacings for both area ratios are those between 0 and 1throat diameter (fig. 6). From a cavitation standpoint, however, nozzle spacings of 1throat diameter o r larger are preferable (fig. 10). If both maximum efficiency and cavitation resistance were design objectives, they could be satisfied by the selection of a nozzle spacing (s/dt) of approximately 1.0. It should be recognized that this cri terion is not universal; optimum nozzle spacing is dependent on throat length and secondary inlet configuration.

Photographs of -.cavitation. - Photographs of various stages of cavitation for both~ ~

area ratios are shown in figure 12. The flow conditions depicted correspond to conditions plotted in figure 7. Visually, there was no significant effect of area ratio on the character of the cavitation. At the fully inserted nozzle position, visible incipient cavitation gener­ally appeared first as isolated voids in midstream (fig. 12(a-l)), appearing and disappear­ing rapidly and randomly. Reductions in inlet p ressure produced well-defined, sustained amounts of cavitation extending downstream from the exit plane of the nozzle (figs. 12(a-2), (a-5), (a-6), (b-2), (b-6), and (b-7)). Further reductions in inlet p ressure caused the cavitating region to increase in downstream length and to spread radially out­ward to the wall (figs. 12(a-3), (a-4), (a-7), (a-8), (b-3), (b-4), and (b-9)). Substantial correlation appeared to exist between the point of performance dropoff and the condition for which the cavitation region contacted the wall. Generous amounts of cavitation could be tolerated before performance was affected.

The cavitation patterns depicted in figures 12(a-9) and (a-10) are typical of the forms of cavitation associated with nozzle spacings greater than zero. At large nozzle spacings (regardless of area ratio), the characterist ics of the cavitation cloud were different from those associated with the fully inserted nozzle position. The cavitation cloud was rela­tively unstable, forming in explosive bursts well downstream of the nozzle exit. As inlet pressure was reduced, the cavitation cloud would frequently extend rapidly upstream and become "attached" to the nozzle. The phenomenon was quite random and not necessarily repeatable, whereas the cavitation patterns observed at the fully inserted nozzle position were comparatively steady and had a high degree of reproducibility.

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(a-1) Nozzle spacing, 0; flow ratio, 3.5; net positive suction head of secondary fluid, 26.1 feet (7.9 m); normalized head ratio, 1.0.

(a-3) Nozzle spacing, 0; flow ratio, 3.5; net positive suction head of secondary fluid, 17.6 feet (5.4 m); normalized head ratio, 1.0.

(a-5) Nozzle spacing, 0; flow ratio, 4.5; net positive suction head of secondary fluid, 30.8 feet (9.4 m); normalized head ratio, 1.0.

(a-7) Nozzle spacing, 0; flow ratio, 4.5; net positive suction head of secondary fluid, 26.8 feet (8.2 m); normalized head ratio, 0.97.

(a-2) Nozzle spacing, 0; flow ratio, 3.5; net positive suction head of secondary fluid, 18.5feet (5.6 m); normalized head ratio, 1.0.

(a-4) Nozzle spacing, 0; flow ratio, 3.5; net positive suction head of secondary fluid, 15.6 feet (4.8 m); normalized head ratio, 1.0.

(a-6) Nozzle spacing, 0; flow ratio, 4.5; net positive suction head of secondary fluid, 28.4 feet (8.7 m); normalized head ratio, 0.97.

(a-8) Nozzle spacing, 0; flow ratio, 4.5; net positive suction head of secondary fluid, 25-7 feet (7.8 m); normalized head ratio, 0.51.

(a-9) Nozzle spacing, 1-05; flow ratio, 3.5; net positive suction head (a-10) Nozzle spacing, 1-05; flow ratio, 3.5; net positive suction of secondary fluid, 10.9 feet (3.3 m); normalized head ratio, 0.99. head of secondary fluid, 10.1 feet 0.1mk; normalized head

ratio, 0.98. (a) Two nozzle positions; area ratio, 0.066.

Figure 12. - Deveiopment of cavitation as secondary ink t head is reduced;

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(b-1) Flow ratio, 1.3; net positive suction head of secondary fluid, 20.6 feet (6.3 m); normalized head ratio, 1.0.

(b-3) Flow ratio, 1-3; net positive suction head of secondary fluid, 14.7 feet (4.5 m); normalized head ratio, 0.92.

(b-5) Flow ratio, 2.0; net positive suction head of secondary fluid, 40.1 feet (12.2 m); normalized head ratio, 0.99.

(b-7) Flow ratio, 2.0; net positive suction head of secondary fluid, 35.9 feet (10.9 m); normalized head ratio, 1.01.

(b-9) Flow ratio, 2.0; net positive suction head of secondary fluid, 33.5 feet (LO. 2 m); normalized head ratio, 0.73.

(b-2) Flow ratio, 1.3; net positive suction head of secondary fluid, 17.1 feet 15-2 m); normalized head ratio, I.03.

(b-4) Flow ratio, 1.3; net positive suction head of secondaryfluid. 14.5 feet (4.4 m); normaIized head ratio, 0.19.

(b-6) Flow ratio, 2.0; net positive suction head of secondary fluid, 37.8 feet (11.5 m); normalized head ratio, 0.99.

(b-8) Flow ratio, 2.0; net positive suction head of secondary fluid, 34.4feet (10.5 m); normalized head ratio, 0.83.

(b) Fully inserted nozzle; area ratio, 0.197; nozzle spacing, 0.

Figure 12. - Concluded.

20

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Predict ion Parameters

Cavitation prediction parameter. - Several parameters which have been presented in the l i terature as jet flow or jet pump cavitation parameters were discussed earlier in the section MECHANISM AND ANALYSIS OF CAVITATION (p. 3). They a r e developed in appendix B sections I to III. It is then shown in appendix B section IV that these parameters a r e related, and that a prediction parameter w can be derived from energy and continuity relations which correlates cavitation-caused total head dropoff points with the secondary- to primary-fluid velocity ratio V3/Vn. This cavitation prediction param­eter is defined as

2g and is plotted as a function of velocity ratio in figure 13 for selected values of secondary inlet friction loss coefficient K,.

The friction loss coefficients K are discussed in reference 3, and Ks is defined by

spacing, ratio, coefficient / Sldt R

0 0 0 1.05) 0.066

P 0 2.58 A 0 h . 9 5 } ,197 7'

3 2.68 .09 1

.1 .2 . 3 5 .6 . 7 Velocity ratio, V31Vn

Figure 13. - Comparison of experimental and theoretical values of prediction parameter.

2 1

Page 26: NASA TECHNICAL NOTE -- NASA TN D-4592

K = p2 - p3 (B1)S YV;-2g

Values of corresponding to points of performance dropoff are plotted in figure 13. Theoretical curves corresponding to several values of secondary friction loss coefficient are also plotted. The curves for Ks = 0.09 (R= 0.066) and Ks = 0.14 (R= 0.197) correspond to measured values of Ks as reported in reference 3. Also plotted for com­parison purposes are curves that would correspond to secondary friction loss coefficients of 0 and 0. 30.

It is apparent that, at the fully inserted nozzle position, the theory generally cor­relates the data, although the data fall slightly above the respective theoretical curves. This suggests that some factor not considered in the analysis had some influence on the cavitation process. As previously observed (Overall Cavitating Performance, Effect of nozzle spacing, p. IS), the wake produced by the pr imary nozzle walls increases the turbulence in the shear layer. The increase in turbulence intensifies the cavitation process and resul ts in a premature deterioration in performance. The higher indicated values of w for the smaller area rat io pump may be attributed to the larger relative size of the wake in that pump. Both nozzles had wall thicknesses of 0.027 inch (0.069 cm). This thickness represented about 421 percent of the nozzle internal diameter for R = 0.197 and 8 percent of the nozzle internal diameter for R = 0.066.

Effect of nozzle spacing: One of the premises of the analysis presented in appendix B section IV was that nozzle spacing is zero. It is therefore somewhat surprising that, for such a wide diversity of flows and area ratios, the values of w for retracted nozzle positions agree so closely.

As discussed previously in the section Overall Cavitating Performance, Effect of nozzle spacing (p. 16), the effect of a retraction of the nozzle from the throat entrance is an increase of static pressure level in the secondary inlet region (with the consequent suppression of cavitation) and a reduction of the effect of nozzle wall thickness. Thus, as is evident from figure 13, retraction of the nozzle ac ts to reduce the effective value of w . Although there is no method for predicting the effect quantitatively, an empirical value of Ks = 0 appears justified for predicting the cavitation dropoff conditions for nozzle spacings of s/dt 2 1.0.

At nozzle spacings less than 1 throat diameter, a value of Ks greater than the actual measured Ks may be necessary to account for the effect of nozzle wall thickness. The amount of "correction" in Ks that would be necessary would depend on the degree of departure from the zero wall thickness assumption.

Comparison with previously reported results: The theoretical curves for Ks = 0 and Ks = 0.30 are presented again in figure 14 together with a plot of the modified

22

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Frict idn loss coefficientII

I''-1for secondary inlet,

I II I t

parameter (reTi'I '.II DI nd:

0 1.05 0 2.58

2.68+E.6

I l . 7

l.5 .1 .2 . 3

Velocity ratio, V31Vn

Figure 14. - Comparison of cavitation data from references 6 and 7 with prediction parameters f rom present report (eq. (B7H and from reference 6.

Rouse parameter (appendix B section III), and data obtained by Mueller (ref. 7), Bonnington (ref. 6), and in this investigation. An examination of figure 14 reveals general agreement between Bonnington's data and the data obtained in the present investigation. There is, however, no agreement with the data reported by Mueller, except at velocity ratios greater than 0.5. It is not completely clear why the je t pumps tested by Mueller cavitated at higher values of w. But it appears that the performance dropoff was ab­normally early and may be related to blockage of the secondary flow area by the primary nozzle external contour. A drawing of the primary nozzle in position in one of the two secondary inlets tested is reproduced from reference 7 in figure 15. The exterior contour of nozzle A creates a converging-diverging secondary inlet area, presenting a greater­than-normal restriction to the secondary flow. Although the nozzle spacing or spacings at which Mueller's cavitation data were taken are not noted specifically in reference 7, numerical examples cited by the author use s = 0.022 inch (0.056 cm). At that nozzle position, a calibration of the secondary inlet region (ref. 7) had indicated extremely high losses (Ks - 0.73). It should therefore not be unexpected that Mueller's pumps exhibited a high susceptibility to cavitation. The apparent correlation between the Mueller data and

23

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4 Axial spacing of pr imary nozzle exit from throat entrance, s

Figure 15. - Schematic drawing of pr imary nozzle and secondary inlet contours used in cavitation tests of reference 7.

Bonnington's modification of the Rouse parameter may only have been coincidental, the direct result of a restricted inlet region. Considering this, and the correlation of the Bonnington data and the data of this investigation with the U parameter (eq. (7)), it may logically be concluded that W is the more valid jet pump prediction parameter.

It should be quite c lear from the foregoing discussion that the external contour of the primary nozzle and the contour of the secondary inlet region a r e extremely impor­tant design parameters. Proper hydrodynamic streamlining will produce lower losses and therefore improved noncavitating performance levels. But, more important, in order to prevent premature cavitation, the secondary flow passage should be smooth and unrestricted, and the nozzle wall thickness should be minimized.

. -Alternate cavitation prediction parameter. - In appendix B section V, an alternate cavitation parameter a is developed (eq. (�38)) which eliminates the need to express cavitation results as a function of velocity ratio. With Q defined as

at the condition of cavitation-induced total headrise dropoff, the one-dimensional applica­tion of the energy equations predicts

24

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Therefore, the value of a! at which the break in performance occurs should correspond to 1.0 plus the value of the secondary inlet friction loss coefficient Ks.

The same data presented in figure 13 were expressed in te rms of ct and presented in figure 16. The ordinate is a ratio of operating head ratio N to the noncavitating value of head ratio NNc at the specified flow conditions, and the parameter ct is expressed as the abscissa. Reduction of net positive suction head of the secondary fluid cor re­sponds to a reduction ,of ct. Therefore, figure 16 may be considered to be analogous to a conventional pump headrise as a function of the net positive suction head characteris­tic.

With few exceptions, performance dropped off at nearly the same values of a for a specific nozzle position. In some cases curved characterist ics resulted af ter dropoff began (i. e. , a increased as performance deteriorated). This was caused by difficulties in maintaining flow rat io constant after performance degradation had begun. Regardless

I IAI"'p7

II

I/

1.6112.4 2.8 3.2 . 8 1.2 2.0 2.4 2.8 3.2 3.6

Cavitation parameter, I

(a-1) Nozzle spacing, 0. (a-2) Nozzle spacing, 1.05.

Cavitation parameter, a

(a-3) Nozzle spacing, 2.58.

(a) Area ratio, 0.066; primary flow rate, 33.0 gallons per minute ( Z . O ~ X ~ O - ~m3/sec).

Figure 16. - Jet pump cavitation performance as funct ion of cavitation parameter.

25

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al

m

1.2 I I I I I 1.0 --LA I I la

V + TI I Iz-z

-z .8 I I I I .-0- I Flow ratio,E M Vg . 6 S rrtVN.--E

.4 0 1.67 0 n 1.7z 0 2.1

. 2 I I I I

0 I I I I I .8 1.2

/1.6 2.0

1

1 II

I I

2.4 2.8 3.2 . 8 1.2 1.6 2.0 2.4

n

2.8

2.0

3.2 3.4

(b-1) Nozzle spacing, 0.

1.2

y 1.0-z z .-0­p .8 V 0)

c .6 .--N

m E g .4

. 2.8

Cavitation parameter, a

(b-2) Nozzle spacing, 0.95.

1.2 1.6 2.0 2.4 2.8 Cavitation parameter, a

(b-3) Nozzle spacing, 2.68.

(b) Area ratio, 0.197; pr imary flow rate, 75.0 gallons per minu te 14. 7 4 x N 3 m3/sec).

Figure 16. - Concluded.

of area ratio o r flow ratio, performance dropped off at values of Q! between 0.9 and 1.0 at moderate to large nozzle spacings (s/dt > 1.0). For fully inserted nozzle positions, the values of Q! at performance dropoff were 1.17 for R = 0.197 and 1.32 for R = 0.066. The values of Ks inferred from figure 16 are identical to the values infer­red from figure 13 (wagainst V3/Vn). This is not unexpected because w = cu(V3/Vn)2 .

SUMMARY OF RESULTS

The cavitation performance of two jet pumps having nozzle- to throat-area ratios of

26

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0.066 and 0.197 was evaluated in a closed loop facility using room-temperature, de­aerated water. Each of the two nozzles was operated at three spacings of the nozzle exit upstream from the throat entrance.

The investigation yielded the following principal results: 1. Two related cavitation dropoff prediction parameters are presented which

correlated the experimental data with reasonable accuracy. For both parameters, it was necessary to use a n empirical loss coefficient for nozzle spacings between 0 and 1 throat diameter. It was possible to neglect this coefficient at larger nozzle spacings.

2. At any fixed nozzle position, higher net-positive-suction head of the secondary fluid was required to suppress cavitation as secondary- to primary-flow ratio was in­creased.

3. At any fixed flow ratio, less net-positive-suction head of the secondary fluid was required to suppress cavitation as the nozzle was retracted from the throat inlet. At nozzle spacings greater than or equal to approximately 1 throat diameter, the cavitation cloud was rather unstable, whereas the cavitation patterns observed at zero nozzle spacing were comparatively steady and had a high degree of reproducibility.

4. Both high efficiency and cavitation resistance were achieved at a nozzle spacing of 1 throat diameter f rom the throat entrance for the test pump configurations evaluated in this investigation.

5. The design of the secondary inlet region, which includes the exterior contour of the primary nozzle, is critical to jet pump cavitation performance. The secondary fluid annular flow path, as described by the secondary inlet contour and the primary nozzle exterior contour, should be hydrodynamically streamlined and smoothly converging to the throat entrance. The primary nozzle wall thickness should be as thin as possible.

6 . As net positive suction head of the secondary fluid was decreased, generous amounts of cavitation were tolerated in the mixing chamber before efficiency and head rat io deteriorated. However, when performance did deteriorate it did so quite sharply.

Lewis Research Center, National Aeronautics and Space Administration,

Cleveland, Ohio, December 13, 1967, 128-31-06-28-22.

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APPENDIX A

SYMBOLS

A

cP C

d

gC H

H s, v

K

L

Z

M

N

N/NNC P

P

PV

Q R

S

V

W

X

f?!

P Y

28

area, f t2; m2

pressure coefficient, (pX- p2)/[y(vn/2g)12

dimensional constant, 448.9 (gal/min)/(ft 3/sec)

diameter, in. ; cm

acceleration due to gravity, 32.163 ft/sec 2 ; 9.803 m/sec2 dimensional constant, 32.174(ft-lb mass)/(sec 2)(lb force); p . 0 (m-kg)/(sec2-N]

total head of fluid, P/y, f t ; m

net positive suction head of secondary fluid, (P2 - pv)/r, f t ; m

friction loss coefficient

length, in. ; cm

throat length, in. ; cm

flow ratio, Q2/Q1

head ratio, (H5 - H2)/(H1 - H5)

normalized head ratio; ratio of operating head ratio to noncaviting head ratio

total pressure, lb force/ft 2 ; N/m 2

static pressure, lb force/ft 2 ; N/m 2

vapor pressure, lb force/ft 2 ; N/m 2

volumetric flow rate, gal/min; m 3/sec

a r e a ratio, An/At

axial spacing of primary nozzle exit from throat entrance, in.; cm

velocity, ft/sec; m/sec

mass flow rate, lb mass/sec; kg/sec

linear distance measured in axial direction from throat entrance, in. ; cm

jet pump cavitation prediction parameter at total headrise dropoff,

(P2 - Pv)/pV2,/2gjJ

diffuser included angle, deg; rad

specific weight, p(g/gc), lb force/ft 3; N/" 3

~ -.... . . .I .

Page 33: NASA TECHNICAL NOTE -- NASA TN D-4592

q efficiency, MN

p fluid density,lb mass/ft 3; kg/m3

uB jet pump cavitation prediction parameter (Bonnington) at total headrise dropoff,

aR free jet incipient cavitation prediction parameter (Rouse), (pF - pv)/[r(V0/2g12

w jet pump cavitation prediction parameter at total headrise dropoff, (P2 - Pv)/p:/2gy

Subscripts :

bep best efficiency point

d

F

f

n

0

P

S

t

ts

X

1

2

3

4

5

diffuser

ambient fluid, free jet

friction

primary nozzle exit plane, jet pump

nozzle exit plane, f ree jet

primary nozzle

secondary fluid inlet

throat

t es t section

linear position measured in axial direction from throat entrance

primary fluid

secondary fluid

location at throat entrance

location at throat exit

location at jet pump discharge

29

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APPENDIX B

DEVELOPMENT OF JET PUMP CAVITATION ANALYSES

The jet pump analyses presented to date share certain common assumptions: (1)Both the primary and secondary fluids are incompressible. (2) The temperatures of the pr imary and secondary fluids are equal. (3) Spacing of the nozzle exit f rom the throat entrance is zero (s/dt = 0). (4) The primary nozzle wall thickness at the exit is ze ro (A3 = At - An). (5) At the point of total headrise dropoff, the static pressure in the throat entrance

plane p3 is equivalent to the vapor pressure of the secondary fluid. Presented in the following sections are three analyses and the resultant parameters

which have been important in the development of jet pump cavitation prediction routines. Two additional parameters are then derived which are related to the previous three.

I. Gosline and O 'Br ien Analysis

Gosline and O'Brien (ref. 4)applied the one-dimensional energy and continuity rela­tions to the secondary fluid and accounted for friction through the use of a dimensionless friction loss coefficient Ks (ref. 3). The nomenclature used in the following equations was established in figures 1 and 17.

where

30

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(a) Jet in ambient f l u id (free jet). Rouse (ref. 5).

(b) Jet pump flow (ducted jet).

Figure 17. - Comparison of nomenclature for free jet and ducted jet.

v3= P 2 - p3

where

A3 = At - An

At the point of total headrise dropoff due to cavitation, it is assumed that static pressure in the exit plane of the nozzle p3 is reduced to its lower limit, that is, vapor pressure pv. Therefore,

Q2 = c A 3 - / F2'(1+ Ks)

31

I

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at the point of total headrise dropoff. The value of Q2 that is calculated from equa­tion (B3) is the limiting value of secondary flow as determined by cavitation.

11. Rouse Parameter

Rouse (ref. 5) utilized a cavitation parameter to correlate incipient cavitation data fo r a free jet (refer to fig. 17(a)). The parameter is conventionally defined as

UR = pF - pv

Y -v:

He observed incipient cavitation to occur at values of uR = 0.6.

111. Bonnington Modified Rouse Parameter

Bonnington attempted to modify Rouse's f ree jet parameter to apply to ducted jets, the case of interest for jet pump flow (ref. 6). In his analysis, he neglected the vapor pressure term in Rouse's parameter, apparently because of its relative insignificance in cold water. It shall be retained here. The following modifications to equation (4) were made by Bonnington (refer to fig. 17(b)):

(1)pF corresponds to p3 2(2) Vo corresponds to Vn, but the denominator y(Vo/2g) corresponds to

y(Vn - V3)2/2g because in a f ree jet the velocity of the entrained fluid V3 is zero, whereas in a ducted je t it has a finite value

Therefore,

UB = p3 - pv

rev, - v3)2

When friction is neglected,

Yv; p3 = p2 -2g

32

Page 37: NASA TECHNICAL NOTE -- NASA TN D-4592

v3

n

2g

2Divide the numerator and the denominator by y(Vn/2g):

Rouse found incipient cavitation to occur when oR = 0.6. Bonnington assumed total head breakdown in a jet pump to occur a lso at a value of 0.6. Setting aB = 0.6 and solving fo r (P2 - Pv)/[(Y/2g) VE] leads to

- p v = 0.6 - 1.2 -+ 1.6 p 3 y-Y 2 -'n2g

This equation is presented graphically in figure 14 as the modified parameter.

IV. Cavitat ion Predict ion Parameter

The parameter proposed in this section is derived in a manner quite s imilar to the Gosline and O'Brien approach. The energy equation applied to the secondary fluid resul ts in

Yv; p2 - p3 = -(1 + Ks)

2g

Page 38: NASA TECHNICAL NOTE -- NASA TN D-4592

-.. .. .. ...

2Divide each side by y(Vn)/2g:

p2 - p3 =gl(l+Ks) Yv;

Define

w = p2 - p3

Yv;

For the fully inserted nozzle position s/dt = 0 and a nozzle wall thickness of zero,

- Q2 An - An'3_ - _ - -Vn A3Q1 At - An

Thus ,

w = = (?J(l+ Ks) = (sr1 - R (1 + Ks)

If it is assumed that, at cavitation dropoff p3 = pv, the parameter 0 becomes

w = - pv = (xr Ks)(1+ Ks) =pJ(l+Yv: 1 - R vn

at the point of total headrise dropoff.

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V. Al ternate Cavitation Predict ion Parameter

Beginning identically to the development of w , n

Yv;Pa - p --(1+ Ks)

3 - 2g

Divide each side by yV:/2g:

p2 - p3 = l + K s YV;-

Define

CY= p2 - p3

If p3 = pv at total headrise dropoff conditions,

C Y = p2 pv = (1 + Ks)

at the point of total headrise dropoff. It should be noted that w = cr(V3/Vn)2. Both w and CY are directly related to the approach presented by Gosline and O'Brien (ref. 4).-

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REFERENCES

1. Sanders, Newel1 D. ; Barrett, Charles A. ; Bernatowicz, Daniel T. ; Moffitt, Thomas P. ; Potter, Andrew E . , Jr. ; and Schwartz, Harvey J. : Power for Spacecraft. Proceedings of the NASA-University Conference on the Science and Technology of Space Exploration. Vol. 2 . NASA SP-11, 1962, pp. 125-150.

2. Chalpin, E. S.; Pope, J. R.; and FOSS,C. L. : Development of a SNAP-8 Pump for Mercury Service. AIAA Specialists Conference on Rankine Space Power Systems. Vol. I. AEC Rep. No. CONF-651026. Vol. 1, pp. 171-185.

3. Sanger, Nelson L. : Noncavitating Performance of Two Low-Area-Ratio Water Jet Pumps Having Throat Lengths of 7.25 Diameters. NASA TN D-4445, 1968.

4 . Gosline, James E. and O'Brien, Morrough P. : The Water Jet Pump. Univ. Cali­fornia Publ. Eng., vol. 3, no. 3, 1933, pp. 167-190.

5. Rouse, Hunter: Cavitation in the Mixing Zone of a Submerged Jet. LaHouille Blanche, vol. 8, Jan.-Feb. 1953, pp. 9-19.

6. Bonnington, S. T. : The Cavitation Limits of a Liquid-Liquid Jet Pump. Publ. RR-605, British Hydromechanics Research Assoc. , Harlow, Essex, England, 1958.

7. Mueller, N. H. G. : Water Jet Pump. Proc. Am. SOC. Civil Eng., J. Hydraulics Div., vol. 90, no. HY3, May 1964, pp. 83-113.

8. Schulz, F. ; and Fasol, K. H. : Wasserstrahlpumpen zur FGrderung von Fllissegkeiten. Springer Verlag, Vienna, 1958.

9. Vogel, R. : Theoretische und Experimentelle Unterschungen as Strahlapparaten. Maschinenbautechnik, Berlin, vol. 5, 1956, pp. 619-637.

10. Holl, J. William; and Wislicenus, George F. : Scale Effects on Cavitation. J. Basic Eng., vol. 83, no. 3, Sept. 1961, pp. 385-398.

11. Eisenberg, Phillip: Mechanics of Cavitation. Handbook of Fluid Dynamics. Victor L. Streeter, ed. , McGraw-Hill Book Co. , Inc. , 1961, pp. 12-2 to 12-9.

12. Frenkel, J. : Kinetic Theory of Liquids. Clarendon Press, Oxford, 1946.

13. Blake, F. G., Jr.: The Onset of Cavitation in Liquids. Tech. Rep. No. 12, Acoustics Research Lab. , Harvard Univ., Sept. 1949.

14. Knapp, Robert T. : Investigation of the Mechanics of Cavitation and Cavitation Damage. Final Rep., Hydrodynamics Lab. , California Inst. Tech. (Contract NONR-22008), June 1957.

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15. Parkin, B. R. ; and Kermeem, R. W. : Incipient Cavitation and Boundary Layer Interaction on a Streamlined Body. Rep. No. E-35.2, Hydrodynamics Lab., California Inst. Tech. , Dec. 1953.

16. Williams, E. E. ; and McNulty, P. : Some Factors Affecting the Inception of Cavita­tion. Cavihtion in Hydrodynamics, National Physical Lab. , Great Britain, Sept. 14-17, 1955.

17. Eisenberg, Phillip: Cavitation. Intern. Sci. Tech., no. 14, Feb. 1963, pp. 72-76, 79-80, 82, 84.

18. Daily, J. W. ; and Johnson, V. E. , Jr. : Turbulence and Boundary-Layer Effects on Cavitation Inception from Gas Nuclei. Trans. ASME, vol. 78, no. 8, NOV. 1956, pp. 1695-1706.

19. Holl, J. William; and Treas te r , A. L. : Cavitation Hysteresis. J. Basic Eng. , vol. 88, no. 1, Mar. 1966, pp. 199-212.

20. Lienhard, J . H. ; and Stephenson, J. M. : Temperature and Scale Effects Upon Cavitation and Flashing in Free and Submerged Jets. J. Basic Eng. , vol. 88, no. 2, June 1966, pp. 525-532.

NASA-Langley, 1968 - 28 E-4115 37

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